Related papers: Moderate deviations on different scales: no relati…
An ordinary differential equation perturbed by a null-recurrent diffusion will be considered in the case where the averaging type perturbation is strong only when a fast motion is close to the origin. The normal deviations of these…
Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a class of stochastic partial differential equations without any…
We obtain the exact large deviation functions of the density profile and of the current, in the non-equilibrium steady state of a one dimensional symmetric simple exclusion process coupled to boundary reservoirs with slow rates. Compared to…
Gaussian couplings of partial sum processes are derived for the high-dimensional regime $d=o(n^{1/3})$. The coupling is derived for sums of independent random vectors and subsequently extended to nonstationary time series. Our inequalities…
Assuming a $q$-variant of the prime $k$-tuple conjecture uniformly, we compute mixed moments of the number of primes in disjoint short intervals and progressions, respectively. This involves estimating the mean of singular series along…
We consider multiple time scales systems of stochastic differential equations with small noise in random environments. We prove a quenched large deviations principle with explicit characterization of the action functional. The random medium…
The characterization of record events is considered for a discrete-time random walk model with long-term memory arising from correlations between successive steps. An important feature is that the correlations are strong enough to give rise…
We derive the sharp non-asymptotical uniform estimations for tails of distributions for classical normed sums of centered normed independent random vectors having a moderate decreasing individual tails of summands.
In this article we introduce associative Look-Up Tables. With their help, pseudo sums are correctly determined. The set of limit distributions in a pseudo-summation scheme of i.i.d. random variables is described. Also, two special cases…
Non-deterministic chaos is a form of low-dimensional dynamics which is characterized by the existence of a countable set of {\em sensitive decision points} (SDP's). Away from these points, the dynamics is well-behaved. Near these points,…
The TASEP (totally asymmetric simple exclusion process) is a basic model for an one-dimensional interacting particle system with non-reversible dynamics. Despite the simplicity of the model it shows a very rich and interesting behaviour. In…
This paper deals with U-statistics of Poisson processes and multiple Wiener-It\^o integrals on the Poisson space. Via sharp bounds on the cumulants for both classes of random variables, moderate deviation principles, concentration…
Random matrices have played an important role in many fields including machine learning, quantum information theory and optimization. One of the main research focuses is on the deviation inequalities for eigenvalues of random matrices.…
We obtain sharp upper and lower bounds for the moderate deviations of the volume of the range of a random walk in dimension five and larger. Our results encompass two regimes: a Gaussian regime for small deviations, and a stretched…
We establish deviation inequalities for the maxima of partial sums of a martingale differences sequence, and of a strictly stationary orthomartingale random field. These inequalities can be used to establish complete convergence of…
The possibility that global discrete dilation invariance is a fundamental symmetry principle of nature is explored. If the discrete self-similarity observed in nature is exact, then the Principle of General Covariance needs to be broadened…
A determinantal approximation is obtained for the permanent of a doubly stochastic matrix. For moderate-deviation matrix sequences, the asymptotic relative error is of order $O(n^{-1})$.
General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…
Non-homogeneous self-similar measures are generically absolute continuous in the domain of parameters for which the similarity dimension is larger than one, see \cite{[SSS]}. Using certain algebraic curves we construct here exceptional…
We model two time and space scales discrete observations by using a unique continuous diffusion process with time dependent coefficient. We define new parameters for the large scale model as functions of the small scale distribution…